Fast Underdetermined DOA Estimation Based on Generalized MRA via Original Covariance Vector Sparse Reconstruction

Geng Wang,Chunlai Yu,Changxiao Chen,Minghao He,Jun Han

doi:10.1109/access.2021.3077080

Abstract

Minimum redundancy array (MRA) has the maximum aperture with continuous difference co-array among various sparse arrays with same number of physical sensors, but it is hard to calculate the sensor position of MRA and realize array design by using MRA. To solve those problem, generalized MRA is proposed with mutual coupling limitation and easy calculation method of sensor position. Based on proposed array configuration, a high-precision underdetermined direction of arrival (DOA) estimation method is proposed with reduced computational complexity. In this method, fast covariance matrix reconstruction is achieved by trace norm minimization with more accurate covariance estimation. Based on the Toeplitz property of covariance matrix in uniform array, a new sparse representation model is established with reduced dimension of covariance vector and faster DOA estimation is achieved via convex optimization. In addition, the proposed method can also be used for underdetermined DOA estimation of other sparse arrays. Using simulation experiments, we demonstrate that the proposed sparse array configuration has superiority over other sparse arrays and the proposed method can outperform most existing methods in terms of underdetermined DOA estimation accuracy and efficiency.

Highlights

Direction of arrival (DOA) estimation based on sparse array has been widely studied in multiple input multiple output (MIMO) radar [1] [2] and underwater acoustic scenarios [3] [4] for the reason that sparse array can achieve direction of arrival (DOA) estimation with more signals than sensors
SIMULATION RESULTS the performance of the proposed generalized minimum redundancy array (GMRA) is compared with the advanced coprime array (CPA), generalized coprime array (GCPA), nested array (NA) under same aperture and the performance of the proposed method original covariance vector sparse representation (OCVSR) for underdetermined DOA estimation with comparison to Covariance matrix interpolation approach (CMIA), Covariance matrix reconstruction approach (CMRA) and covariance matrix sparse representation (CMSR) is evaluated
There are K equal-power uncorrelated far-field narrowband signals which are assumed to be uniformly distributed in [−53.02◦, 53.02◦] unless otherwise stated, and DOAs are not restricted to lie on the pre-defined grids so signals are in off-grid model just like [45]

Summary

Introduction

Direction of arrival (DOA) estimation based on sparse array has been widely studied in multiple input multiple output (MIMO) radar [1] [2] and underwater acoustic scenarios [3] [4] for the reason that sparse array can achieve DOA estimation with more signals than sensors. Several new sparse array structures with closed form expression were proposed, such as the nested array (NA) [6] [7], coprime array (CPA) [8]– [10], generalized coprime array (GCPA) [11], super nested array (SNA) [12], generalized nested array (GNA) [13] and their combinations [14] These sparse arrays all have less consecutive virtual sensors in the difference co-array [15]– [18] than the MRA under the same number of physical sensors while the number of consecutive virtual sensors is the main factor of underdetermined DOA estimation performance. The proposed array is more suitable for array designing than the MRA

Methods

Results

Conclusion